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Chapter 9: Problem 12

Find the perimeter of each square. $$ 56.9 \mathrm{~km} \text { on a side } $$

Short Answer

Expert verified
The perimeter of the square is 227.6 km.

Step by step solution

01

- Identify the Given Information

The length of one side of the square is given as 56.9 kilometers. Denote this length as \( s = 56.9 \) km.
02

- Understand the Formula for Perimeter of a Square

The perimeter \( P \) of a square can be calculated using the formula: \[ P = 4s \] where \( s \) is the length of one side of the square.
03

- Substitute the Given Length into the Formula

Substitute \( s = 56.9 \) km into the formula: \[ P = 4 \times 56.9 \]
04

- Calculate the Perimeter

Perform the multiplication to find the perimeter: \[ P = 4 \times 56.9 = 227.6 \] Therefore, the perimeter of the square is 227.6 kilometers.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

perimeter calculation
Calculating the perimeter of a square is a straightforward process. The perimeter is the total distance around the edge of the square. You need to know the length of one side. Then, use the formula: \[ P = 4s \] Here, \(P\) stands for perimeter, and \(s\) is the length of one side. For instance, if one side of a square is 56.9 kilometers, you simply multiply 4 by 56.9. This multiplication gives you the perimeter. In this case, it is \[ 4 \times 56.9 = 227.6 \] So, the perimeter is 227.6 kilometers. The formula works because a square has four equal sides.
geometry
Geometry is a branch of mathematics that studies shapes, sizes, and properties of spaces. Understanding geometry helps in many areas. A square is a basic geometric shape. Each side of a square is equal in length, and it has four right angles.
  • Perimeter: The total length around any shape.
  • Square: A four-sided polygon with all sides equal and all angles right.
  • Right Angle: An angle of 90 degrees.
By knowing these basics, calculating properties like the perimeter becomes easier.
square properties
To understand how to calculate the perimeter, you need to know the properties of a square. A square is a unique polygon.
  • It has four equal sides.
  • Each angle in a square is 90 degrees.
  • The diagonals of a square are equal and bisect each other at right angles.
These properties ensure that when you calculate the perimeter by the formula \[ P = 4s \], it is always accurate. Because all sides are the same, multiplying one side by 4 gives the perimeter. Another key property is symmetry. Any side can be used in the perimeter formula, making the calculation simple.
mathematical formulas
Formulas in mathematics help solve problems quickly. For squares, the perimeter formula \[ P = 4s \] is essential. Here's why:
  • Efficiency: Formulas save time. Knowing \[ P = 4s \] means you don't have to add all four sides individually when calculating the perimeter.
  • Consistency: Using a formula ensures your results are always reliable, as long as you use it correctly.
  • Simplicity: Mathematical formulas break down complex problems into simple operations.
For students, learning and applying these formulas is crucial. It lays the foundation for more advanced math topics. Understand the logic behind formulas to use them effectively. In the case of the square, the formula is derived from its symmetrical properties. Remember, math formulas are tools. The more you practice, the more proficient you become.

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